I am working with a group currently using aging hardware and MS Office versions. Vector looks like it will work on the hardware and it comes with Abiword and Gnumeric. I assume these would be reasonable substitutes for MS Word and Excel but please correct me if I am wrong.

MS Access is more heavily used so I am asking for recommendations / suggestions for an alternative that works well on Vector. Open Office would be my first guess but is it available for Vector? If so, I hope the installation is straightforward because my skills in that respect are minimal.

I don't think Gnome-Office (which has abiword and gnumeric) includes a database program like Access or Paradox or Approach. However, both OpenOffice.org and LibreOffice do. The equivalents in these programs are:Writer = WordCalc = ExcelBase = AccessImpress = Powerpoint

As nicdm mentioned, LibreOffice is packaged in Gslapt, so it is very easy to install.

For the latest or for localized builds (IE, in a different language) of either LibreOffice or OpenOffice.org, see this post (it's easier to just use Gslapt, though).